The telescreen serves several purposes. In regards to 1984's characters, it is a monitoring device for Big Brother. Winston does not know for certain that he is always being watched, but he must presume that he is in order to survive. Ideologically, if a government wants to control its subjects, it must constantly monitor them so that it can curb anyone who does not fall in line with party policy--the telescreen provides the Inner Party with that power.
Orwell also uses the telescreen to get his readers to think about the role that technology could play in their future. The book, published in 1949, might seem a little ahead of its time, but no doubt a savvy Orwell observed all of the technological advances being made around him and considered just how dangerous that technology could be when used by those who seek absolute power.